Introduction

Now that we have derived Maxwell's equations as he himself derived them, let us do everything backwards, starting with Maxwell's equations and regarding them simply as a set of vector equations relating the vector fields E, D, B, H and J. Therefore, initially we ascribe no physical significance to these fields. We then make a minimum number of postulates in order to give them physical significance and so derive from them all the experimentally established laws of electromagnetism. This approach is taken by Stratton in his book Electromagnetic Theory.

We can then apply Maxwell's equations to further aspects of electromagnetic theory – the properties of electromagnetic waves, the emission of waves by accelerated charges, and so on – which provide tests of the theory that go far beyond the empirically derived laws from which Maxwell's equations were deduced. If the theory were to prove to be inconsistent with experiment then the interlocking nature of many of the results, as illustrated below, indicates how the whole edifice would have to be changed.

A number of my colleagues have objected strenuously to this approach to electromagnetism, principally on the grounds that historically it is most unlikely that anyone would have discovered Maxwell's equations by this route. I am not prepared to speculate about that. What I do know is that this procedure of starting with a mathematical structure, which is then given physical meaning, is found in other aspects of fundamental physics, for example in the theory of linear operators and quantum mechanics and in tensor calculus and the special and general theories of relativity.